The 23-year-old Swedish free agent will sign with the Dallas Stars in the next 24 hours, his agent, J.P. Barry, told Sun Media this afternoon.
It's a blow to the Leafs, who were hoping to insert Brunnstrom among their top forwards.
"There were no bad options for him," Barry said. "Dallas, he felt, was the most comfortable fit."
Though numerous NHL teams had expressed an interest, the Stars and Leafs were in the final four contenders along with the Detroit Red Wings and Montreal Canadiens.
"It was more of a situation of why it would be Dallas than why it would not be Toronto, Detroit or Montreal," Barry said. "The Leafs were willing to give him a good opportunity to play."
Brunnstrom had nine goals and 28 assists in 54 games last season for Farjestad in the Swedish Elite League.
The Stars will meet the Red Wings in the Western Conference final starting tonight.